This paper was presented at the AIChE - SPE Joint Symposium on Multiphase Flow in the Production and Drilling of Oil Wells, September 25–28, 1960, in Tulsa, Oklahoma
The addition of water to crude oil pipelines appears to be an important method for decreasing the pressure gradient for a given oil throughput. Although the concentric oil-in-water flow pattern provides the greatest possible reduction, the general case, in which the liquids are stratified as a result of the oil and water having different densities, is also characterized by reductions in pressure gradient.
To evaluate the magnitude of the pressure gradient reduction to be expected in stratified flow systems, the Navier-Stokes equations were solved by a numerical procedure utilizing a digital computer, for the laminar stratified flow of two Newtonian liquids - oil and water - in a circular pipe. Liquid flow rates were obtained for the flow of five hypothetical oils ranging in viscosity from 4 to 1500 centipoises in the presence of water, by computing the oil and water velocity profiles for a series of arbitrary oil-water interface positions. It was found that the maximum values for the pressure gradient reduction factor ranged from 1.12 to 1.31 for the five oils and occurred at water contents ranging from 12 to 93 per cent respectively.
The computed reduction factors were considerably lower than experimental values and this appears to indicate that wave motion and mixing at the oil-water interface produces a further and very significant reduction in the pressure gradient.